How can I cook a full chicken with skin on it when my oven is broken?

If you are intent on cooking the bird whole (as opposed to butchering it into pieces which you can fry in a pan), then your only option would be to braise the bird in a large pot, preferably a Dutch oven. There are myriad recipes online; search for "Chicken in a Pot" or "Braised Whole Chicken". As ElendilTheTall mentioned in the comments above, the only other option to keep the chicken whole would be to use a barbecue/grill.

If you don't have a large pot and can't follow ESultanik's recommendation, you're going to need to joint the chicken. Once that's done, you can either shallow fry it (where the oil only comes up a little more than half way up the pieces) or braise it.

If you're going to braise it, I'd actually recommend using a recipe that makes better use of the cooking liquid, such as Arroz con Pollo, where you brown the chicken first, then finish the chicken in the same liquid that you're cooking rice in.

You're also likely going to want to remove the skin -- braising and other wet cooking methods will result in flabby skin, which is typically not good. You can either get your hand under the skin at the neck & lower cavity to loosen it and then slice it off before jointing it (which might make it easier to see where to cut for jointing), or you can just grab and pull (if you can't grip it well, try using a paper towel).

Do you have a big pot with lid or a pressure cooker?

If the chicken fits inside, just put some veggies in the bottom, the chicken, a cup of liquid, salt pepper and herbs and cook it covered during one hour at low fire (maybe 45 minutes if you are using a pressure cooker). Make sure the liquid doesn't evaporate completely or you will burn it; but if you are cooking it slowly, covered with the lid, that shouldn't happen. Once it is ready, you can put the veggies and the rest of the liquid in the blender to make a light sauce, but I would get rid of the fat on top.

If you have time, I would recommend that you cook it the day before, letting it rest in a cool place and then keep it in the fridge, with the sauce, until the next day. You can reheat it in the same pot. It will be more soft and juicy.

Recipes:

I sometimes cook it with some chopped onions, carrots and leak and the juice of a couple of oranges, then I put the skin of the squeezed oranges inside of the chicken, and I add a bit of water.

Another option would be to use white wine instead of oranges, and some rosemary and thyme. Maybe a bit of fennel too.

Enjoy!

You can also spratchcock the chicken (remove the backbone) put in a heavy preferably cast iron, weight it down for a "Brick Chicken" plenty of recipes on the net. This also speeds up the cook time by about 1/2.

A recipe I tried recently (which came out delicious) is murgh mussalam which is a stuffed chicken dish from India (apparently developed in the kitchen of one of the Mughal emperors). Some versions of the recipes call for cooking in the oven but others (like the one I used) have you cook it on the stove. It's probably best used if the chicken is smaller although it would work with a larger bird I suppose if your pot is large enough and you cook it a little longer.

Basically you prepare a stuffing with some minced meat, herbs and spices and stuff it into the cavity of the chicken (along with some hard-boiled although I left them out). The you prepare a curry sauce/gravy on the stove, add in the chicken and cook it covered for about half an hour or until cooked through, stirring every few minutes or so, and spooning over some of the sauce.

This was the recipe I used: https://www.youtube.com/watch?v=UliEDkccxts

You can roast a chicken in a large toaster oven. The chicken will turn out just as good as when you use a conventional oven. Some key points - put the breast down. In a toaster oven the top of the chicken is closer to the heating rods than a traditional oven, so the breast may dry out if you expose it. Here is a video of a chicken roasted in a toaster oven.

https://www.youtube.com/watch?v=nFReZBCg_QQ

Toaster ovens are very cheap. You should be able to find a decent one for around $30 - $70. They are also very energy efficient compared to a traditional oven. Over the long hall, it will pay for itself in reduced utility bills. Preheating a toaster oven takes only a few minutes. I often use the toaster oven to roast vegetables, bake cookies, make open face sandwiches, reheat pizza slices and roast chickens.

I've had some success playing with Jamie Oliver's poached chicken recipe. It's pretty much a one-pot dish, but clearly you can't do it in a frying pan. You will have very limited options for cooking a whole chicken in just a frying pan, especially if you mean a simple shallow-sided frying pan rather than a higher sided sauté pan.

Frying Pan

Sauté Pan

Considering you want to keep the chicken whole, and you won't necessarily want to buy a slow cooker or a Dutch Oven, I recommend using a relatively deep frying pan with a lid.

Place the chicken in the frying pan, and fill the pan until about halfway up the chicken's sides with warm water, seasoned with spices and salt, with a few tablespoons of vinegar. The vinegar will break down some of the proteins of the chicken and will help it to be 'fall off the bone', the salt will help to loosen the connection between skin and meat, and the water will help heat to permeate deeper into the chicken. Leave to cook on medium-low heat with the lid on, with the mixture barely boiling. You will need to rotate the chicken, spoon liquid on top of it, and rotate it occasionally. It should take a little more than 1 hour.

If you want crispy skin, then I'm afraid I don't have a method, just a guess to try searing it in hot oil.

Depending on the size, you may be able to cook the whole chicken in a crockpot. I'd estimate it would take 3-4 hours on High.

I would cook a chicken tabaka. It is a whole chicken flattened on the frying pan and fried in some oil. The dish is very simple and results is something quite similar to an oven-cooked chicken. All you have to do is to cut the chicken to separate the ribcage. The bird remains in one piece.